Let E,F be two Polish spaces and [X_n,Y_n],[X,Y] random variables with values in E×F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E×F, the conditional expectation of f(X_n,Y_n) given Y_n converges in distribution to the conditional expectation of f(X,Y) given Y.

Convergence results for conditional expectations

Crimaldi I;
2005-01-01

Abstract

Let E,F be two Polish spaces and [X_n,Y_n],[X,Y] random variables with values in E×F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E×F, the conditional expectation of f(X_n,Y_n) given Y_n converges in distribution to the conditional expectation of f(X,Y) given Y.
2005
conditional expectation; weak convergence of probability measures; Skorohod's theorem
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/4013
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